Theorem el0321old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el0321old.1	⊢ 𝜑
	el0321old.2	⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
	el0321old.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion	el0321old	⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		el0321old.1	⊢ 𝜑
2		el0321old.2	⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
3		el0321old.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4	2	dfvd3ani	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )
5	1 4 3	eel0321old	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜂 )
6	5	dfvd3anir	⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )